The Ultrafast Quantum Dynamics of Photoexcited Adenine–Thymine Basepair Investigated with a Fragment-based Diabatization and a Linear Vibronic Coupling Model

In this contribution we present a quantum dynamical study of the photoexcited hydrogen bonded base pair adenine–thymine (AT) in a Watson–Crick arrangement. To that end, we parametrize Linear Vibronic Coupling (LVC) models with Time-Dependent Density Functional Theory (TD-DFT) calculations, exploiting a fragment diabatization scheme (FrD) we have developed to define diabatic states on the basis of individual chromophores in a multichromophoric system. Wavepacket propagations were run with the multilayer extension of the Multiconfiguration Time-Dependent Hartree method. We considered excitations to the three lowest bright states, a ππ* state of thymine and two ππ* states (La and Lb) of adenine, and we found that on the 100 fs time scale the main decay pathways involve intramonomer population transfers toward nπ* states of the same nucleobase. In AT this transfer is less effective than in the isolated nucleobases, because hydrogen bonding destabilizes the nπ* states. The population transfer to the A → T charge transfer state is negligible, making the ultrafast (femtosecond) decay through the proton coupled electron transfer mechanism unlikely, in line with experimental results in apolar solvents. The excitation energy transfer is also very small. We carefully compare the predictions of LVC Hamiltonians obtained with different sets of diabatic states, defined so to match either local states of the two separated monomers or the base pair adiabatic states in the Franck–Condon region. To that end we also extend the flexibility of the FrD-LVC approach, introducing a new strategy to define fragments diabatic states that account for the effect of the rest of the multichromohoric system through a Molecular Mechanics potential.


Contents
S-2 S1 Additional Computational Details S1.1 On the different references states for diabatization Figure S1: A pictorial representation of the three different choices of the references states adopted for diabatization in St-LVC, FrD(MM ref )-LVC and FrD-LVC parameterization for two states localized on Adenine. In FrD-LVC, these states are computed for the isolated Adenine in the geometry it has in the AT ground state minimum. FrD(MM ref )-LVC is similar to FrD but the reference states are computed accounting for the effect of the thymine at MM level (for single-point calculations this is equivalent to describe thymine as a set of charges, we chose RESP protocol). In St-LVC we adopt as reference states the adiabatic states of the AT base pair computed at the ground state geometry. They are denoted with the same labels of the fragment states they resemble most. Of course this is possible in AT where the adiabatic states are already well-localized, but may not be possible in general. In fact, in other systems (e.g. stacked dimers of nucleobases) such states might be strongly delocalized, making impossible establishing a one-to-one correspondence with fragment states. S-3

S1.2 Absorption Spectra
For the st-LVC model, the transition dipoles of the diabatic states µ [d] are simply those of the adiabatic states of the MC. For the FrD-LVC approaches, the transition dipole moments of the diabatic states at the reference geometry may be obtained by applying the transformation matrix D, defined in Eq. 5 in the main text, to the diagonal matrix of adiabatic transition dipole moments of the MC at reference geometry µ[a MC ] Then, for both st-LVC and FrD-LVC approaches, the absorption spectra (ω) at zero Kelvin, can be expressed in a TD framework as: ij (ω) = auto (ω) + cross (ω) (S2) where N A is Avogadro's number, c 0 is the speed of light in vacuo, 0 is the vacuum permittivity and we introduced a quadratic damping ruled by a parameter Γ, corresponding to a Gaussian broadening in the frequency domain. We represent the diabatic transition dipole moments with the shorthand µ d gj for the transition from ground state g to diabatic state d j in the above. The diabatic transition dipole moment is considered independent of the nuclear coordinates (Condon approximation), and the ground-vibrational state of the ground electronic state is represented by 0 and its energy is set to zero.
The auto ( auto ) and cross (

A-T(CT)
A(n N π)2 Figure S2: Convergence test for ML-MCTDH propagations with respect to the number of single particle functions (SPFs). We considered the nonadiabatic dynamics of electronic populations of AT in gas phase predicted with FrD(MM ref )-LVC Hamiltonians parameterized at the FC point with CAM-B3LYP calculations. The time evolution adopted with the settings used in most of the calculations ( "standard", solid line) is compared with what obtained decreasing both the number of SPFs (dash line). A graphical representation of the multilayer (ML) trees is reported in Figure S3. Similar tests were done modifying the dimension of the primitive basis set, showing also in this case a good convergence. Data not reported  Figure S3: Graphical representation of a typical ML-MCTDH tree adopted in the computations (top) and with smaller basis set and number of SPFs adopted to check the convergence of the calculations made with standard settings (bottom) S3 Further results S3.1 FC point , in eV, with respect to S 0 in the FC point), weight of the predominant diabatic state in adiabatic state for both FrD(MM ref )-LVC and FrD-LVC (W RESP , W isolated ), and oscillator strengths δ OPA , computed for AT at the FC point. CAM-B3LYP/6-31G(d) calculations. This is an extended version of the Table 1 in the main text, showing also the predominant transition coefficients in terms of the Kohn-Sham orbitals. Orbital numbering shown in Figure S4.  Figure S4: Schematic drawing of the main Kohn-Sham molecular orbitals of AT involved in the electronic transitions discussed in the present paper, computed at CAM-B3LYP/6-31G(d) level of theory with isovalue 0.04.    (0)) and electronic couplings (E D ij (0)) of A' diabatic states of AT in C s symmetry at ground state equilibrium geometry from the FrD(MM ref )-LVC 12 model (eV). Results for the FrD-LVC model in parentheses.
T(ππ * 1) 5.336 ( (0)) and electronic couplings (E D ij (0)) of A" diabatic states of AT in C s symmetry at ground state equilibrium geometry from the FrD(MM ref )-LVC 12 model (eV). Results for the FrD-LVC model in parentheses.

S3.1.1 L a and L b states of Adenine
Inspection of Table S1 and Figure 2 in the main text show that S 3 and S 4 are clearly associated to two bright excited states localized on A, the latter being slightly more intense of the former. In the isolated Adenine in its ground state minimum, L a is expected to be the stronger absorbing state with a dominant H→L character, and L b the weaker absorbing one with a dominant H→L+1 character. S3 The relative position of these two bands is still the subject of a very lively debate, since different methods give different predictions. S3,S4 For isolated A, in the geometry that it appears in the AT minimum (i.e. the geometry used for the reference states in the FrD-LVC approach), Figure S5 shows that at the selected level of theory, the two main configurations H→L, H→L+1 are strongly mixed in the two bright adiabatic states. However, the most stable and most absorbing state is the one with larger H→L component, which we therefore we label as L a .
In the base pair, this picture appears to be switched, as the lower energy state (S 3 ) is less absorbing and with a greater H→L+1 component, corresponding to the transition between KS orbitals of 76→79. The higher energy state (S 4 ), is more absorbing, and has a larger component from the KS orbitals 76→78 corresponding to H→L in isolated A.
For A in the field of the RESP charges of T (i.e. the procedure used for the reference states in the FrD(MM ref ) approach) things are again different. As in the base pair, the more stable state (S 1 ) is the weaker, but in this case its H→L coefficient is larger than H→L+1, whereas S 2 is more intense but with a larger component H→L+1.
The overlap matrices computed in the diabatization procedure provide a way to quantitatively asses the correspondence between the A-like states in AT and those of the isolated monomer (see Table S1) The projections of the L a and L b states in the FrD-LVC approaches on S 3 and S 4 of the base pair are respectively 94% and 93%. For FrD(MM ref )-LVC reference states these projections become 98% and 95%. Whereas the above projections are large and therefore assignments are robust, it is noteworthy that the overlap matrix (see Table S6) also indicates that the TD-DFT states of the base pair (and therefore also the diabatic states of the St-LVC model) actually have S-11 some small components from the other state of Adenine (L b or L a ) and even from the lowest ππ * state of T. Table S6: Overlaps between the TD-DFT adiabatic states of the base pair computed at the FC position and the local diabatic states corresponding to the first bright state of Thymine, T(ππ * ), and the first two bright states of Adenine, A(L a ) and A(L b ), as defined with Standard, FrD or  Figure S5: Electronic character and main orbital transitions corresponding to states we label as L a , L b and n N π * states in the adiabatic set (TD-DFT on the baseair)(left) and diabatic basis set (TD-DFT on single base Adenine) in the field of RESP charges(middle) and without RESP charge(right).
S-13 Table S7: Norm of coupling vector λ ij · λ ij for 12 diabatic state LVC models of AT in C s symmetry at ground state equilibrium geometry. Differences between the models are highlighted in bold.

S3.2 Adiabatic and Diabatic Minima
In order to investigate further the coupling of A(L a ), A(L b ) and their relative stability with respect A(n N π * 1) we computed the TD-DFT adiabatic states of the base pair at the minima of the A(L a ), A(L b ) and A(n N π * 1) diabatic states, as predicted by the FrD(MM ref )-LVC model. As shown in Figure S6, the minimum of A(L a ) lies at 5.11 eV, very close to the predicted LVC adiabatic state from all three procedures (see Table 3 in the main manuscript). The minimum of A(L b ) lies on the contrary at 5.40 eV, ∼ 0.1 eV above what predicted by the LVC models (which however shows that the adiabatic state is quite mixed). Finally A(n N π * 1) is predicted to lie at 5.03 eV, with a further moderate stabilization with respect to what predicted by St-LVC and FrD(MM ref )-LVC models, and a much more significant stabilization than with respect to FrD-LVC minimum. Starting from the geometries of these diabatic minima we also attempted a re-optimization of these three states with TD-DFT (data reported in Figure S7). We were able to locate both the A(L a ) and A(n N π * 1) minima and found that they exhibit only a very slight stabilization (∼ 0.03 eV) indicating that the minimum geometries estimated by LVC are quite accurate. The optimization algorithm failed to of optimize A(L b ), ending instead in the A(L a ) minimum.  Figure S7: Energies of the lowest-energy planar adiabatic excited state minima mostly localized on A from TD-DFT excited state geometry optimisations. It is noteworthy that the TD-DFT adiabatic states energies of L a , L b and n N π * 1 obtained either in the diabatic minima or after a TD-DFT optimization are very similar (Compare this with Figure S6.)

S-19
Table S10 : Energies E D ii of the diabatic states i on all predicted diabatic minima of AT in C s symmetry in gas phase obtained from different LVC models with 12 states and CAM-B3LYP/6-31G(d) parametrization.   Figure S8: Diabatic state populations for 1-methylthymine following initial excitation to T(ππ * 1) (top), and for 9-methyladenine following initial excitation to A(L a ) (middle) and A(L b ) (bottom). For both bases, 6 state St-LVC models are utilised, parametrized by CAM-B3LYP/6-31G(d). S-21

S3.3.2 Population of CT: AT vs GC
In both AT and GC the reorganization energy of CT state is about 1.15 eV. The CT state is energetically closer to other bright excited states in GC than AT, with CAM-B3LYP/6-31G(d) predicting the CT state to be ≈0.2 eV more stable than the lowest bright states for GC, whilst it is ≈0.7 eV less stable than the lowest bright states for AT, as shown in Table S12. Moreover, Table   S11 shows that diabatic electronic coupling of the G→C(CT) state with G(L a ) is much greater than the coupling of the A→T(CT) state with A(L a ). Furthermore, the sum of the couplings for the ππ * states of G and C to the G→C(CT) state is greater than the sum of the couplings for the ππ * states of A and T to the A→T(CT) state.    (0), as well as diabatic energies at predicted diabatic excited state planar minima (D min ) and adiabatic energies at the FC point from TD-DFT. All computations parametrized by CAM-B3LYP/6-31G(d).  6.14 6.14 6.14 6.14 6.13 6.08 7.A(n N π * 2) 6.15 6.15 6.15 6.15 6.15 6.14 8.T(n O π * 2) 6.44 6.44 6.44 6.44 6.44 6.44 9.A(n N π * 3) 6.63 6.63 6.63 6.63 6.63 6.61 10.T(ππ * 2) 6.67 6.64 6.64 6.64 6.64 6.62 11.T(ππ * 3) 6.73 6.73 6.73 6.73 6.73 12.A(ππ * 3) 6.81 6.81 6.81 6.81 6.81        (0)) and electronic couplings (E D ij (0)) of A' states from the FrD(MM ref )-LVC 22-state model of AT in C s symmetry at ground state equilibrium geometry (eV).   (0)) and electronic couplings (E D ij (0)) of A" states from the FrD(MM ref )-LVC 22-state model of AT in C s symmetry at ground state equilibrium geometry (eV).  A→T(CT1) 6.16 6.16 6.16 6.16 6.15 6.14 6.08 7 A(n N π * 2) 6.21 6.21 6.17 6.17 6.16 6.16 6.14 8 T(n O π * 2) 6.45 6.45 6.45 6.45 6.45 6.44 6.44 9

S3.5.2 FrD-LVC calculations
A(n N π * 3) 6.66 6.65 6.64 6.64 6.63 6.64 6.61 Table S20: Norm of coupling vector λ ij · λ ij for 22 state FrD-LVC model of AT in C s symmetry at ground state equilibrium geometry, parametrized with CAM-B3LYP/6-31G(d).      (0)) and electronic couplings (E D ij (0)) of A' states from the FrD-LVC 22-state model of AT in C s symmetry at ground state equilibrium geometry (eV).   (0)) and electronic couplings (E D ij (0)) of A" states from the FrD-LVC 22-state model of AT in C s symmetry at ground state equilibrium geometry (eV).